The prediction of stochastic crack growth accumulation is important for the reliability analysis of structures as well as the scheduling of inspection and repair/replacement maintenance. Because the initial crack size, the stress, the material properties and other factors that may affect the fatigue crack growth are statistically distributed, the fi rst-order second-moment technique is often adopted to calculate the fatigue reliability of industrial structures. In this paper, a second-order thirdmoment technique is presented and a three-parameter Weibull distribution is adopted to refl ect the infl uences of skewness of the probability density function. The second-order third-moment technique that has more characteristics of those random variables that are concerned in reliability analysis is obviously more accurate than the traditional fi rst-order second-moment technique.
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Based on a random sample from the Weibull distribution with unknown shape and scale parameters, lower and upper prediction limits on a set of m future observations from the same distribution are constructed. The procedures, which arise from considering the distribution of future observations given the observed value of an ancillary statistic, do not require the construction of any tables, and are applicable whether the data are complete or Type II censored. The results have direct application in reliability theory, where the time until the first failure in a group of m items in service provides a measure regarding the operation of the items, as well as in service of fatigue-sensitive aircraft structures to construct strategies of inspections of these structures; examples of applications are given.
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For important fatigue-sensitive structures of aircraft whose breakdowns cause serious accidents, it is required to keep their reliability extremely high. In this paper, we discuss inspection strategies for such important structures against fatigue failure. The focus is on the case when there are fatigue-cracks unexpectedly detected in a fl eet of aircraft within a warranty period (prior to the fi rst inspection). The paper examines this case and proposes stochastic models for prediction of fatigue-crack growth to determine appropriate inspections intervals. We also do not assume known parameters of the underlying distributions, and the estimation of that is incorporated into the analysis and decision-making. Numerical example is provided to illustrate the procedure.
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